Heat a small nonstick skillet over medium heat. Add 2/3 lb. ground chicken and cook, stirring frequently, until chicken is opaque and just cooked through, about 2 minutes.
Transfer chicken to a plate and let cool.
Combine cooked chicken, remaining 1 1/3 lb. chicken, scallions, miso, and 2 tablespoons oil in a large bowl.
Knead with your hands until a homogenized, sticky mixture forms, about 5 minutes.
Clean hands; lightly coat with oil to prevent meat mixture from sticking. Divide mixture into 16 equal portions. Roll each into a ball, then form each ball into a 4"-long cylinder onto 2 skewers (hold 2 skewers, separating 1" apart at top to form a V shape).
Press meat gently to flatten slightly.
Repeat with remaining skewers and meat.
Over a medium-hot fire in a charcoal grill, gas grill on high. Arrange bricks for yakitori grill.
Working in batches, grill skewers, turning every minute, for 4 minutes. Brush with tare and continue cooking, turning once, for 2 minutes. Brush again with tare and grill, turning once, until cooked through, about 2 minutes longer.
They can be eaten right off the sticks or slid off the stick into a piece of lettuce.